[1602.02215] Swivel: Improving Embeddings by Noticing What's Missing

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Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods."/> <meta name="twitter:site" content="@arxiv"/> <meta name="twitter:card" content="summary"/> <meta name="twitter:title" content="Swivel: Improving Embeddings by Noticing What's Missing"/> <meta name="twitter:description" content="We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate..."/> <meta name="twitter:image" content="https://static.arxiv.org/icons/twitter/arxiv-logo-twitter-square.png"/> <meta name="twitter:image:alt" content="arXiv logo"/> <link rel="stylesheet" media="screen" type="text/css" href="/static/browse/0.3.4/css/tooltip.css"/><link rel="stylesheet" media="screen" type="text/css" href="https://static.arxiv.org/js/bibex-dev/bibex.css?20200709"/> <script src="/static/browse/0.3.4/js/mathjaxToggle.min.js" type="text/javascript"></script> <script src="//code.jquery.com/jquery-latest.min.js" type="text/javascript"></script> <script src="//cdn.jsdelivr.net/npm/js-cookie@2/src/js.cookie.min.js" type="text/javascript"></script> <script src="//cdn.jsdelivr.net/npm/dompurify@2.3.5/dist/purify.min.js"></script> <script src="/static/browse/0.3.4/js/toggle-labs.js?20241022" type="text/javascript"></script> <script src="/static/browse/0.3.4/js/cite.js" type="text/javascript"></script><meta name="citation_title" content="Swivel: Improving Embeddings by Noticing What's Missing" /><meta name="citation_author" content="Shazeer, Noam" /><meta name="citation_author" content="Doherty, Ryan" /><meta name="citation_author" content="Evans, Colin" /><meta name="citation_author" content="Waterson, Chris" /><meta name="citation_date" content="2016/02/06" /><meta name="citation_online_date" content="2016/02/06" /><meta name="citation_pdf_url" content="http://arxiv.org/pdf/1602.02215" /><meta name="citation_arxiv_id" content="1602.02215" /><meta name="citation_abstract" content="We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods." /> </head> <body class="with-cu-identity"> <div class="flex-wrap-footer"> <header> <a href="#content" class="is-sr-only">Skip to main content</a>  <div class="columns is-vcentered is-hidden-mobile" id="cu-identity"> <div class="column" id="cu-logo"> <a href="https://www.cornell.edu/"><img src="/static/browse/0.3.4/images/icons/cu/cornell-reduced-white-SMALL.svg" alt="Cornell University" /></a> </div><div class="column" id="support-ack"> <span id="support-ack-url">We gratefully acknowledge support from the Simons Foundation, <a href="https://info.arxiv.org/about/ourmembers.html">member institutions</a>, and all contributors.</span> <a href="https://info.arxiv.org/about/donate.html" class="btn-header-donate">Donate</a> </div> </div> <div id="header" class="is-hidden-mobile"> <a 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href="https://arxiv.org/search/cs?searchtype=author&query=Shazeer,+N" rel="nofollow">Noam Shazeer</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Doherty,+R" rel="nofollow">Ryan Doherty</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Evans,+C" rel="nofollow">Colin Evans</a>, <a href="https://arxiv.org/search/cs?searchtype=author&query=Waterson,+C" rel="nofollow">Chris Waterson</a></div> <div id="download-button-info" hidden>View a PDF of the paper titled Swivel: Improving Embeddings by Noticing What's Missing, by Noam Shazeer and 3 other authors</div> <a class="mobile-submission-download" href="/pdf/1602.02215">View PDF</a> <blockquote class="abstract mathjax"> <span class="descriptor">Abstract:</span>We present Submatrix-wise Vector Embedding Learner (Swivel), a method for generating low-dimensional feature embeddings from a feature co-occurrence matrix. Swivel performs approximate factorization of the point-wise mutual information matrix via stochastic gradient descent. It uses a piecewise loss with special handling for unobserved co-occurrences, and thus makes use of all the information in the matrix. While this requires computation proportional to the size of the entire matrix, we make use of vectorized multiplication to process thousands of rows and columns at once to compute millions of predicted values. Furthermore, we partition the matrix into shards in order to parallelize the computation across many nodes. This approach results in more accurate embeddings than can be achieved with methods that consider only observed co-occurrences, and can scale to much larger corpora than can be handled with sampling methods. </blockquote>  <div class="metatable"> <table summary="Additional metadata"> <tr> <td class="tablecell label">Comments:</td> <td class="tablecell comments mathjax">9 pages, 4 figures</td> </tr> <tr> <td class="tablecell label">Subjects:</td> <td class="tablecell subjects"> <span class="primary-subject">Computation and Language (cs.CL)</span></td> </tr><tr> <td class="tablecell label">Cite as:</td> <td class="tablecell arxivid"><span class="arxivid"><a href="https://arxiv.org/abs/1602.02215">arXiv:1602.02215</a> [cs.CL]</span></td> </tr> <tr> <td class="tablecell label"> </td> <td class="tablecell arxividv">(or <span class="arxivid"> <a href="https://arxiv.org/abs/1602.02215v1">arXiv:1602.02215v1</a> [cs.CL]</span> for this version) </td> </tr> <tr> <td class="tablecell label"> </td> <td class="tablecell arxivdoi"> <a href="https://doi.org/10.48550/arXiv.1602.02215" id="arxiv-doi-link">https://doi.org/10.48550/arXiv.1602.02215</a><div class="button-and-tooltip"> <button class="more-info" aria-describedby="more-info-desc-1"> <svg height="15" role="presentation" xmlns="http://www.w3.org/2000/svg" viewBox="0 0 512 512"><path fill="currentColor" d="M256 8C119.043 8 8 119.083 8 256c0 136.997 111.043 248 248 248s248-111.003 248-248C504 119.083 392.957 8 256 8zm0 110c23.196 0 42 18.804 42 42s-18.804 42-42 42-42-18.804-42-42 18.804-42 42-42zm56 254c0 6.627-5.373 12-12 12h-88c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h12v-64h-12c-6.627 0-12-5.373-12-12v-24c0-6.627 5.373-12 12-12h64c6.627 0 12 5.373 12 12v100h12c6.627 0 12 5.373 12 12v24z" class=""></path></svg> <span class="visually-hidden">Focus to learn more</span> </button>  <div role="tooltip" id="more-info-desc-1"> <span class="left-corner"></span> arXiv-issued DOI via DataCite</div> </div> </td> </tr></table> </div> </div> </div> <div class="submission-history"> <h2>Submission history</h2> From: Chris Waterson [<a href="/show-email/961e9ddf/1602.02215" rel="nofollow">view email</a>] <br/> <strong>[v1]</strong> Sat, 6 Feb 2016 04:39:41 UTC (522 KB)<br/> </div> </div>  <div class="extra-services"> <div class="full-text"> <a name="other"></a> <span class="descriptor">Full-text links:</span> <h2>Access Paper:</h2> <ul> <div id="download-button-info" hidden> View a PDF of the paper titled Swivel: Improving Embeddings by Noticing What's Missing, by Noam Shazeer and 3 other authors</div><li><a href="/pdf/1602.02215" aria-describedby="download-button-info" accesskey="f" class="abs-button download-pdf">View PDF</a></li><li><a href="/src/1602.02215" class="abs-button download-eprint">TeX Source</a></li><li><a href="/format/1602.02215" class="abs-button download-format">Other Formats</a></li></ul> <div class="abs-license"><a href="http://arxiv.org/licenses/nonexclusive-distrib/1.0/" 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[1602.02215] Swivel: Improving Embeddings by Noticing What's Missing